Hierarchical Structure and Self-gravity in the Rosette Molecular Cloud

We analyze the hierarchical structure in the Rosette Molecular Cloud (RMC) using $^{13}$CO J=1-0 data from the Milky Way Imaging Scroll Painting (MWISP) survey with a non-binary Dendrogram algorithm that allows multiple branches to emerge from parent structures. A total of 588 substructures are identified, including 458 leaves and 130 branches. The physical parameters of the substructures, including peak brightness temperature ($T_{\rm peak}$), brightness temperature difference ($T_{\rm diff}$), radius ($R$), mass ($M$), velocity dispersion ($\sigma_v$), and surface density ($\Sigma$), are characterized. The $T_{\rm peak}$ and $T_{\rm diff}$ distributions follow exponential functions with characteristic values above $5\sigma_{\rm RMS}$. The statistical properties and scaling relations, i.e., $\sigma_v$-$R$, $M$-$R$, and $\sigma_v$-$R\Sigma$ relations are in general consistent with those from traditional segmentation methods. The mass and radius follow power-law distributions with exponents of 2.2-2.5, with slightly flatter slopes for substructures inside the HII region. The velocity dispersion scales weakly with radius ($\sigma_v \propto R^{0.45\pm 0.03}$, $r = 0.58$), but shows a tighter correlation with the product of surface density and size ($\sigma_v \propto (\Sigma R)^{0.29\pm 0.01}$, $r = 0.73$). Self-gravitating substructures are found across scales from $\sim$0.2 to 10 pc, and nearly all structures with peak brightness above 4 K are gravitationally bound ($\alpha_{\rm vir} < 2$). The fraction of bound structures increases with mass, size, and surface density, supporting the scenario of global hierarchical collapse (GHC) for the evolution of molecular clouds, in which molecular clouds and their substructures are undergoing multiscale collapse.